Method for calibrating a plurality of data channels in a vector sensor

ABSTRACT

A system, processor and method of use for calibration processing is provided to calibrate acoustic vector sensor data collected at comparatively close range. Vector sensor data collected at close range includes data collected with source-to-receiver separations ranging from a one-tenth to approximately two acoustic wavelengths. The calculations substantially account for the acoustic impedance of a spherically diverging wave front, where the curvature is sufficiently pronounced to cause errors in resulting measurements in the calculations. The processing uses information contained within the vector sensor data to increase the accuracy of the vector sensor data.

This application is a divisional of pending prior U.S. patentapplication Ser. No. 13/200,035 filed on Sep. 7, 2011 entitled “A SYSTEMFOR SELF-LOCALIZING NEAR DATA FIELD PROCESSING” by the inventor, StevenE. Crocker. This divisional application claims the benefit under 35U.S.C. §121 of the prior application's filing date.

STATEMENT OF GOVERNMENT INTEREST

The invention described herein may be manufactured and used by or forthe Government of the United States of America for governmental purposeswithout, the payment of any royalties thereon or therefor.

CROSS REFERENCE TO OTHER PATENT APPLICATIONS

None.

BACKGROUND OF THE INVENTION

(1) Field of the Invention

The present invention relates to correcting an estimated range of asource-to-sensor distance in response to a range difference error thatis determined by comparing and processing data collected in a near field(or otherwise) from a sensor and from a reference.

(2) Description of the Prior Art

Often, equipment such as hydrophones are tested and calibrated duringthe manufacturing and operational phases of the life cycle of theequipment. As such, test equipment for hydrophone applications isarranged in various locations relative to the units of the equipmentundergoing testing. Common difficulties encountered while performing thetests include measuring the various distances between and amongstacoustic sources and reference hydrophones and the units under test.Errors in measurement of the distance affect the accuracy of themeasurements made, and thus degrade equipment performance when theequipment is not optimally calibrated. Furthermore, relative motionamong the acoustic source, reference hydrophone and the unit under testaffects the accuracy of the measurements made.

SUMMARY OF THE INVENTION

Accordingly, it is a primary object and general purpose of the presentinvention to increase the accuracy of empirical measurements.

It is a further object of the present invention to provide an efficientmethod for using information contained within empirical measurements toincrease the accuracy of the empirical measurements.

In accordance with the present invention, calibration processing is usedto calibrate acoustic vector sensor data collected at close range. Forexample, vector sensor data (collected at close range) includes datacollected with source-to-receiver separations ranging from one-tenth toapproximately two acoustic wavelengths. The calculations substantiallyaccount for the acoustic impedance of a spherically diverging wavefront; where the curvature is sufficiently pronounced to causesubstantial errors in resulting measurements in the calculations. Theprocessing uses information contained within the vector sensor data toincrease the accuracy of the vector sensor data. Thus, there is provideda processor for calibrating acoustic vector sensor data collected atclose range (as well other ranges).

The above and other features of the invention, including various noveldetails of construction and combinations of parts, will now be moreparticularly described with reference to the accompanying drawings andpointed out in the claims. It will be understood that the particularassembly embodying the invention is shown by way of illustration onlyand not as a limitation of the invention. The principles and features ofthis invention may be employed in various and numerous embodimentswithout departing from the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects, features and advantages of the present invention will beapparent with reference to accompanying drawings in which is shown anillustrative embodiment of the invention, wherein correspondingreference characters indicate corresponding parts throughout the severalviews of the drawings and wherein:

FIG. 1 is a diagram of a system implementing one embodiment of thepresent invention;

FIG. 2 is a graph illustrating range difference error estimation in anembodiment of the present invention;

FIG. 3 is a graph illustrating range difference error in data to beprocessed by an embodiment of the present invention;

FIG. 4 is a graph illustrating range measurement error propagation indata to be processed in accordance with the present invention;

FIG. 5 is another graph illustrating range difference error estimationin an embodiment of the present invention;

FIG. 6 is a graph illustrating range difference error estimationcorrections in an embodiment of the present invention; and

FIG. 7 is another diagram illustrating range difference error estimationcorrections in an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Referring now to the drawings, and more particularly to FIG. 1, adiagram of a test system is illustrated and referenced by numeral 10.The test system 10 includes an acoustic source 12 for providing a sourceof propagated acoustic waves. Reference hydrophone 14 is arranged havinga source-to-receiver distance of approximately two to four meters. Boththe acoustic source 12 and the reference hydrophone 14 are submerged atan example depth of approximately 14.5 meters.

Vector sensor 16 is, for example, an acoustic vector sensor module (unitunder test) that is arranged in Test Setup A at a first location that isapproximately two meters from both the acoustic source 12 and thereference hydrophone 14; thus forming an equilateral triangle with eachside being two meters in length. Vector sensor 16 a is arranged in TestSetup B at a second location that is approximately two meters from thevector sensor 16 and four meters from the acoustic source 12. The vectorsensor 16 a in various embodiments may be the vector sensor 16 moved toa new location or may be a different vector sensor, such as a vectorsensor arranged with other vector sensors in a towed sensor array.

Self-localizing near field data processor 18 is arranged to receive areference sample set of collected data from the reference hydrophone 14and is arranged to receive a sensor sample set of collected data fromthe vector sensor 16 (and optionally the vector sensor 16 a). The nearfield data processor 18 is also arranged to determine a range differenceerror in response to a comparison of the reference sample set ofcollected data and the sensor sample set of collected data. The nearfield data processor 18 uses the range difference error to correct atleast partially an estimated range of the source-to-sensor distance.Thus, FIG. 1 describes an example data collection geometry used tocalibrate equipment that includes the vector sensors 16 and 16 a.

The relative positions of one or more acoustic sources (e.g., theacoustic source 12), one or more reference hydrophones (e.g., thereference hydrophone 14), and one or more vector sensors (e.g., thevector sensors 16 and 16 a) in the illustrated data collection geometryare variable in accordance with the teachings disclosed herein. Forexample, the data collection geometry can be used to test performance ofa towed array of acoustic vector sensors that arranged using a varietyof materials and manufacturing approaches. As discussed below, theperformance of a given configuration is determined using the complexsensitivity of the scalar and vector channels of acoustic vector sensorsinstalled in the test system 10.

Calibration waveforms used for these experiments typically includegated, continuous wave signals ranging from 100 to 1000 Hz. Nominalpulse widths range from 35 to 50 milliseconds. Typical pulse repetitionfrequencies (PRF) are often approximately two to four Hertz. The sensormodule is typically rotated through a full rotation to fully sample thedipole response pattern of the vector channel and to determine theorientation. Calibration wave forms are thus transmitted throughout aportion or all of a rotation of a vector sensor. Data is collectedthroughout the rotation.

A typical objective of each test is to collect data in an acoustic nearfield that is used to compute the frequency-dependent, complexsensitivity of the scalar and vector sensor data channels for a givenconfiguration. The complex sensitivity is computed using acoustic(scalar pressure) and vector (acceleration) channels in an acousticvector sensor that provide data collected in the acoustic near field. Asused herein, an acoustic near field exists at source-to-receiverseparations that are sufficiently short such that the specific acousticimpedance of the wave front is not well-approximated by the plane waveimpedance. Thus, analyses of data collected in the near-field may showinconsistencies when compared against analyses of data collected havingphysically (and accurately) measured geometries.

Calibration calculations that depend on data collected in the near fieldare often sensitive to range measurement errors in the acoustic nearfield because a given error in the measured source-to-receiver rangeproduces an error in the computed sensitivity magnitude that varies as afunction of the inverse of the absolute source-to-receiver range. Theimpact of range measurement errors are thus magnified in the acousticnear field.

Calibration calculations that depend on data collected in the near fieldare also often sensitive to range measurement errors in the acousticnear field because the specific acoustic impedance is a strong functionof the wave number-range product (kr) in the acoustic near field. As aresult, calculation of the reference vector field quantities based onscalar reference measurement (e.g., using a reference hydrophone) isnormally critically dependent on having an accurate physical measurementof the source-to-receiver ranges. The dependencies are especiallycritical when the imaginary part of the complex acceleration sensitivity(e.g., phase response) is used where the specific acoustic impedancevaries rapidly as a function of the wave number-range product (kr).

Conventional methods for the calibration of acoustic vector sensor towedarrays have operated on data collected at nominal source-to-receiverseparations of approximately fifty meters. At these ranges the specificacoustic impedance of the field produced by a compact acoustic source atintermediate frequencies (100≦f≦1000 Hz) is well-approximated by theplane wave impedance. Typical wave number-range products (kr) for thesetests have a range from 30 to 440. However, array calibrations conductedusing these methods show that the vector channels of point sensorsinclude an erroneous phase response characteristic that is notconsistent with the phase of the incident acoustic vector field.Subsequent developmental testing on short sensor modules (which isrepresentative of typical towed arrays arranged using given techniques)can be conducted at source-to-receiver separations of two to fourmeters. At these ranges and frequencies (0.85≦kr≦15); the acoustic fieldis not well-approximated using plane wave modeling.

Calibration calculations are disclosed herein for processing acousticvector sensor data collected at close range. In an embodiment, vectorsensor data collected at close range includes data collected withsource-to-receiver separations ranging from one-tenth to approximatelytwo acoustic wavelengths. Thus, calculations are disclosed (that aresuitable for the calibration of test articles), substantially accountfor the acoustic impedance of a spherically diverging wave front, wherethe curvature is sufficiently pronounced to cause substantial errors inresulting measurements in the calculations. The calculations in thedisclosed embodiment assume that the aperture of the acoustic source iscompact with respect to an acoustic wavelength produced by the acousticsource.

The acoustic field generated by a compact acoustic source includes ascalar field. The scalar field presented to the reference hydrophone andthe vector sensor is represented using Equation [1], (in which theassumed harmonic time dependence has been suppressed):

$\begin{matrix}{P_{ref} = {{\frac{P_{o}}{r_{ref}}{\mathbb{e}}^{{- j}\;{kr}_{ref}}{and}\mspace{14mu} P_{uut}} = {\frac{P_{o}}{r_{uut}}{\mathbb{e}}^{{- j}\;{kr}_{uut}}}}} & \lbrack 1\rbrack\end{matrix}$where:

P_(ref) is the acoustic pressure at the reference hydrophone;

P_(uut) is the acoustic pressure at the unit under test;

P_(o) is the acoustic pressure at a reference distance from the source;

r_(ref) is the source-to-reference hydrophone range;

r_(uut) is the source-to-unit under test range (acoustic vector sensor);and

k is the acoustic wave number.

The complex pressure sensitivity of the reference hydrophone and thevector sensor are represented as the ratio of the voltage output by thesensor to the acoustic pressure at the sensor (Equation [2]):

$\begin{matrix}{M_{ref} = {{\frac{v_{ref}}{P_{ref}}{and}\mspace{14mu} M_{{uut}_{0}}} = \frac{v_{{uut}_{0}}}{P_{uut}}}} & \lbrack 2\rbrack\end{matrix}$where:

M_(ref) is the complex sensitivity of the reference hydrophone;

M_(uut) ₀ is the complex sensitivity of the vector sensor scalar(hydrophone) channel, in which the sensitivity and voltage for thescalar channel of the vector sensor (hydrophone) is indicated with thesubscript “0” to identify the measured field variable as a tensor oforder zero;

v_(ref) is the complex voltage measured on the reference hydrophone; and

v_(uut) ₀ is the complex voltage measured on the vector sensor scalar.

Combining Equations [1] and [2] provides the complex sensitivity of thevector sensor hydrophone (e.g. the scalar channel) provided as Equation[3].

$\begin{matrix}{M_{{uut}_{0}} = {M_{ref}\frac{v_{{uut}_{0}}r_{uut}}{v_{ref}r_{ref}}{\mathbb{e}}^{j\;{k{({r_{uut} - r_{ref}})}}}}} & \lbrack 3\rbrack\end{matrix}$

The complex exponential of Equation [3] compensates for the phasebetween the reference and the vector sensor hydrophone when thesource-to-receiver paths are unequal. Given the maturity and longexperience in using hydrophones and hydrophone-based arrays; theimaginary parts (phase angles) of the sensitivities can be expected tobe relatively small.

Moving from determining complex pressure sensitivity to determiningcomplex acceleration sensitivity; the complex sensitivity of a vectorchannel is represented as the ratio of voltage output by the sensor tothe measured field variable, which in this case is the acoustic particleacceleration shown in

$\begin{matrix}{\mspace{301mu}{{M_{{uut}_{1}} = \frac{v_{{uut}_{1}}}{a_{uut}}},}\mspace{250mu}} & \lbrack 4\rbrack\end{matrix}$where:

M_(uut) ₁ is the complex sensitivity of the vector, in which thequantities are annotated with the subscript “1” below to identify themeasured field variable as a tensor of order one;

V_(uut) ₁ is the voltage measured on a vector sensor channel(acceleration); and

a_(uut) is the incident acoustic particle acceleration

$\frac{\partial u}{\partial t}.$

In contrast to the equations provided for the hydrophone channels,Euler's momentum equation is used to determine the acoustic particleacceleration from the gradient of the acoustic pressure (shown asEquation [5]), where μ is the fluid density:

$\begin{matrix}{\frac{\partial u}{\partial t} = {\frac{- 1}{\rho}{\nabla p}}} & \lbrack 5\rbrack\end{matrix}$

The compact sound source (discussed above) is assumed to produce anacoustic wave spreading spherically (from a relatively compact aperture)into free space (e.g., a practically infinite medium). The validity ofthe assumed infinite medium is verified by gating the receivedcalibration waveforms to ensure exclusion of reflections from the watersurface and other boundaries (such as test equipment, test tank, and thelike).

The spherical wave is described using a standard spherical coordinatesystem. In spherical coordinates, the acoustic field produced by acompact source in free space normally depends only on range. Thus, termsfor the angular components of the gradient (shown in Equation [6])vanish:

$\begin{matrix}{{\nabla p} = {{\frac{\partial p}{\partial r}\hat{r}} + {\frac{1}{r}\frac{\partial p}{\partial\theta}\hat{\theta}} + {\frac{1}{r\;\sin\;\theta}\frac{\partial p}{\partial\phi}\hat{\phi}}}} & \lbrack 6\rbrack\end{matrix}$where

{circumflex over (r)}, {circumflex over (θ)}, {circumflex over (φ)} areunit vectors in standard spherical coordinates; and

r, θ, φ are displacements in their respective coordinate directions.

Combining the gradient of Equation [1] with Equation [5] forms Equation[7], which depicts the radial component of the acoustic vector field ata point related to the scalar field. As discussed above, the angularcomponents of the vector field vanish when a compact source in freespace is used.

$\begin{matrix}{\frac{\partial u}{\partial t} = {\frac{k}{\rho}\left( {\frac{1}{kr} + j} \right)p}} & \lbrack 7\rbrack\end{matrix}$

Accordingly, combining Equations [1], [2], [4] and [7] yields anexpression for determining the complex sensitivity of an acousticaccelerometer at a first location (e.g., the acoustic vector sensor);using the acoustic pressure measure at a different location (e.g., thereference hydrophone) as the reference. The expression for determiningthe complex sensitivity of an acoustic accelerometer at one location isgiven as Equation [8]:

$\begin{matrix}{M_{{uut}_{1}} = {M_{ref}\frac{v_{{uut}_{1}}r_{uut}}{v_{ref}r_{ref}}\frac{\rho}{k}\left( \frac{{kr}_{uut}}{1 + {j\;{kr}_{uut}}} \right){\mathbb{e}}^{j\;{k{({r_{uut} - r_{ref}})}}}}} & \lbrack 8\rbrack\end{matrix}$

Calculation of the complex pressure sensitivity depends on accurateknowledge of the ranges of the source-to-reference and thesource-to-unit under test. For Equations [3] and [8] to produce validresults in a near field; the ranges need to be known with sufficientprecision. However, in many test situations, it is difficult todetermine and/or control the ranges with the precision required toprevent the propagation of errors into the amplitude and phase of thecomplex sensitivities for both the scalar and vector channels.

For example, errors in the reported ranges have been manifested as aphase difference of a signal that is received by both the reference andvector sensor hydrophones when both the reference and vector sensorhydrophones were reported to have been at equal distances from thesource (which ideally does not have a phase difference). The error inphase tends to be manifest as a linear trend as illustrated in FIG. 2.

FIG. 2 is a plot showing a phase error of the reception of a signalbetween a vector sensor hydrophone and a reference hydrophone that arenot both the same range (e.g., distance) from the source of the signal.Plot 20 includes a horizontal axis 22 and a vertical axis 24. Horizontalaxis 22 represents a wavenumber k (in inverse meters); whereas, thevertical axis 24 represents a measured difference in phase between thereception of a signal between a vector sensor hydrophone and a referencehydrophone. Samples 26 (designated generally with small circles) areillustrated as the phase difference as a function of the wavenumber.Line 28 is a linear approximation of the set of the observed samples 26and has slope δr of −14.2 cm.

The observed linear trend in phase (illustrated by line 28) is largelythe result of a time delay between receptions of the signal at locationshaving different distances. Given that these signals were collected atnearly the same time (e.g., sample-for-sample), a likely explanation ofthe delay is there being differing lengths of propagation of the signalpaths. Thus, the phase error occurs because the actual distancesinvolved were different than the reported (e.g., expected) geometry ofthe test setup.

FIG. 3 is a plot showing an estimated range difference error of thereception of a signal as a vector sensor module is rotated using a testfixture. Plot 30 includes a horizontal axis 32 and a vertical axis 34.The horizontal axis 32 represents an azimuth, whereas the vertical axis34 represents an estimated range difference between the vector sensorand the reference hydrophones. Samples 36 (designated generally withsolid dots) are illustrated as the range difference as a function of theazimuth of a test-fixture support pole that is rotated to change theorientation of the vector sensor during testing. For example, the sample38 of the set of observed samples indicates an average range differenceof approximately −18.5 cm at an azimuth of approximately 220 degrees.

Thus, the estimated range difference error varies over the course of onefull revolution of the pole to which the vector sensor module wasmounted. A peak-to-peak range variation of approximately sevencentimeters is observed for the set of the samples 36 over onerevolution. For the depiction of FIG. 3, the support pole from which thevector sensor module was deployed was found during post-test inspectionto be bent (thus causing translation of the vector sensor duringrotation of the pole). Accordingly, the bent pole contributed to theobserved variation in range as the vector sensor module was rotatedthrough one full revolution (e.g., 360 degrees).

While the data support estimation of range difference errors, the datadoes not directly provide information about the extent to which theerror may have been due to placement of the source, the reference or theunit under test. Also, the wave impedance is a strong function of rangein the acoustic near field (as shown with reference to FIG. 4).

FIG. 4 is a plot showing range measurement propagation errors in phaseand magnitude. Curve 40 (interpolated from sampled data from varioustest ranges having differing minimum and maximum ranges) representsphase errors of wave impedance relative to a plane travelling wave asplotted in accordance with a horizontal axis 42 (wavenumber-range: kr)and a vertical axis 44 (phase error in degrees). Curve 46 (interpolatedfrom sampled data) represents magnitude errors of wave impedancerelative to the plane travelling wave as plotted in accordance with thehorizontal axis 42 and a vertical axis 48 (magnitude error in decibels).The curves 40 and 46 demonstrate substantial errors in phase andmagnitude, respectively, in near field measurements (e.g., aroundwavenumber-ranges of ten or less), with the magnitude of the errorsincreasing exponentially as the wavenumber-range approaches zero. Thus,accurate source-receiver separations are useful in preventing thepropagation of significant errors to the complex accelerationsensitivity. Also, the disclosed techniques can still be used toincrease accuracy of data sampled at a near field “boundary” andlocations beyond (albeit with the improvement in accuracy decreasingwith an increase in distance).

In accordance with the present disclosure, range measurement errors inthe acoustic near field are detected, estimated and corrected. Thecalibration equations, Equation [3] and [8], are modified to includecorrections to the source-to-reference and/or source-to-unit under testranges. The modified equations (the complex pressure sensitivity andcomplex acceleration sensitivity) are provided as Equation [9] and [10]respectively. The modifications include a first term for correcting theestimated range difference error (δr) and a second term (η) to controlhow that error is apportioned between the source-to-reference andsource-to-unit under test ranges.

$\begin{matrix}{M_{{uut}_{0}} = {M_{ref}\frac{v_{{uut}_{0}}}{v_{ref}}\frac{r_{uut} + {{\eta\delta}\; r}}{r_{ref} + {\left( {\eta - 1} \right)\delta\; r}}{\mathbb{e}}^{j\;{k{({r_{uut} - r_{ref} - {\delta\; r}})}}}}} & \lbrack 9\rbrack \\{{M_{{uut}_{1}} = {M_{ref}\frac{v_{{uut}_{1}}}{v_{ref}}\frac{r_{uut} + {{\eta\delta}\; r}}{r_{ref} + {\left( {\eta - 1} \right)\delta\; r}}\frac{\rho}{k}\left( \frac{k\left( {r_{uut} + {{\eta\delta}\; r}} \right)}{1 + {j\;{k\left( {r_{uut} + {\eta\;\delta\; r}} \right)}}} \right){\mathbb{e}}^{j\;{k{({r_{uut} - r_{ref} - {\delta\; r}})}}}}}{{where}\text{:}}{{\delta\; r\mspace{14mu}{is}\mspace{14mu}{the}\mspace{14mu}{range}\mspace{14mu}{difference}\mspace{14mu}{error}};{and}}{\eta\mspace{14mu}{is}\mspace{14mu} a\mspace{14mu}{control}\mspace{14mu}{parameter}\mspace{14mu}{\left( {0 \leq \eta \leq 1} \right).}}} & \lbrack 10\rbrack\end{matrix}$

Selection of the parameter (η) allows for control of the way that rangedifference error is allocated. For example, setting η=1 allocates theerror to the source-to-unit under test range. Setting η=0 allocates theerror to the source-to-reference hydrophone range. Allocation of theerror equally between the two may be implemented by setting η=½.

The use of η allows experimental conditions to be taken into account.For example, the locations of the source and reference hydrophone can becontrolled by a permanent fixture. In addition, the mean rangedifference error can be observed to change between data collection runswhen the unit under test is removed, modified and reinstalled. Thetime-varying part of the range difference error is correlated to therotation of the unit under test about its longitudinal axis of the unit.Therefore, it can be concluded that the range difference errors are dueto the placement and manipulation of the unit under test. As a result,the control parameter η can be set to allocate the difference error tothe unit under test (η=1).

FIG. 5 is a diagram illustrating-estimated range error in accordancewith differing measuring techniques (e.g., bare sensor versus fullassembly sensors). In fashion similar to FIG. 3; FIG. 5 illustratesestimated range errors of the reception of a signal as a vector sensormodule is rotated (e.g., reoriented) using a test fixture. Plot 50includes a horizontal axis 52 and a vertical axis 54. The horizontalaxis 52 represents an azimuth (of the vector sensor module hydrophoneorientation) whereas the vertical axis 54 represents an estimated rangedifference between the vector sensor module and the referencehydrophones. Samples 56 (designated generally with a circular icon forsamples obtained using a bare sensor, and a triangular icon for samplesobtain using a full assembly) are illustrated as the range difference asa function of the azimuth of a pole that is rotated to change theorientation of the vector sensor during testing. For example, sample 58of the set of the observed samples 56 indicates an average rangedifference of −18.5 centimeter at an azimuth of approximately 220degrees.

The collected data illustrated in the plot 50 is subsequently processedusing the calibration equations disclosed in Equations [9] and [10].

The methods described herein can be used to track the range measurementerror on a “ping-by-ping” basis. That is, for each gated acousticsignal, a range measurement error can be determined for each of thesensors used to receive the gated acoustic signal. Thus, for a givendata set, range difference errors are used to compute the rangecorrection term (δr) for the calibration equations for each sensor. Therange difference errors can also be selectively allocated to the testfixture and/or the unit under test (by using the control parameter η).Calibration results for the scalar measurements and one vector channelare illustrated in FIG. 6 and FIG. 7.

FIG. 6 is a plot illustrating sensitivity and phase errors of hydrophonedata processed using the self-localization methods and system inaccordance with the invention. Curve 60 (interpolated from sampled datapoints) represents phase errors of wave impedance relative to a gatedacoustic signal as plotted in accordance with a horizontal axis 62(frequency in Hertz) and a vertical axis 64 (phase error in degrees).Curve 66 (interpolated from sampled data) represents hydrophonesensitivity to the gated acoustic signal as plotted in accordance withthe horizontal axis 62 and a vertical axis 68 (magnitude error indecibels, volts, microPascals, and the like). The curves 60 and 66demonstrate substantial correction of errors in phase and magnitude;respectively, to data collected in near field measurements (e.g., aroundwavenumber-ranges of ten or less).

FIG. 7 is a plot illustrating sensitivity and phase errors of unit undertest data processed using the self-localization methods and system inaccordance with the invention. Curve 70 (interpolated from sampled datapoints) represents phase errors of wave impedance relative to a gatedacoustic signal as plotted in accordance with a horizontal axis 72(frequency in Hertz) and a vertical axis 74 (phase error in degrees).Curve 76 (interpolated from sampled data) represents unit under testsensitivity to the gated acoustic signal as plotted in accordance withthe horizontal axis 72 and a vertical axis 78 (magnitude error indecibels, volts, microPascals, and the like). Curves 70 and 76demonstrate substantial correction of errors in phase and magnitude,respectively, to data collected in near field measurements (e.g., aroundwavenumber-ranges of 10 or less).

The error bars in FIG. 6 and FIG. 7 represent plus and minus onestandard deviation in the estimated parameter. As shown by the curve 60,the hydrophone phase error is nearly zero (as was indicated in thederivation of the range error difference error correction given above).In an embodiment, the linear phase between the reference and unit undertest hydrophones was assumed to result from time delay/propagation pathlength differences. The remaining (non-linear) phase difference wasallocated to the unit under test (using parameter η).

In various embodiments of the invention, accurately measured distancesbetween the source-to-reference and source-to-unit under test are usedto verify range corrections (based on self-localizing methods andsystems disclosed herein) of acoustic data.

For example, one embodiment uses the self-localizing disclosed hereinwhile performing the data collection task in the acoustic near fieldrelates to the requirement to collect data that is free of surfacereflections. A method of increasing the time between the initial arrivalof a calibration waveform, and the arrival of the surface reflection isto increase the depth at which the test is conducted whilesimultaneously decreasing the source-to-receiver range. Therefore, evenin a large body of water (which generally entails additional expenseover smaller test facilities) that can support data collection in theacoustic far field, it may be desirable to work in the near field inorder to maximize the collection of data that adequately approximatesfree field propagation conditions.

It will be understood that many additional changes in the details,materials, steps and arrangement of parts, which have been hereindescribed and illustrated in order to explain the nature of theinvention, may be made by those skilled in the art within the principleand scope of the invention as expressed in the appended claims.

The foregoing description of the preferred embodiments of the inventionhas been presented for purposes of illustration and description only. Itis not intended to be exhaustive nor to limit the invention to theprecise form disclosed; and obviously many modifications and variationsare possible in light of the above teaching. Such modifications andvariations that may be apparent to a person skilled in the art areintended to be included within the scope of this invention as defined bythe accompanying claims.

What is claimed is:
 1. A method for calibrating a plurality of datachannels in an acoustic vector sensor for simultaneously measuringacoustic pressure and particle motion in at least one direction in apoint in space, said method comprising the steps of: providing a fielddata processor; receiving with the data processor, a reference sampleset of collected data from a reference hydrophone that is arrangedhaving a source-to-reference distance along a first direction whereinthe reference sample set of collected data is produced by sampling anacoustic signal representing the acoustic pressure generated by theacoustic source; receiving with the data processor, a sensor sample setof collected data from the vector sensor that is arranged having anacoustic source-to-sensor distance along a second direction that isdifferent from the first direction wherein the sensor sample set ofcollected data is produced by sampling acoustic signals representing theacoustic pressure and particle motion generated by the acoustic source;determining a range difference error in response to a comparison of thereference sample set of collected data and the sensor sample set ofcollected data of the vector sensor; correcting at least partially anestimated range difference error; correcting at least partially theacoustic pressure observed at the vector sensor; and correcting at leastpartially the particle motion observed at the vector sensor; wherein thevector sensor is calibrated based on said correcting steps.
 2. Themethod in accordance with claim 1, wherein the source-to-sensor distanceis corrected using a complex pressure sensitivity determined inaccordance with the equation$M_{{uut}_{0}} = {M_{ref}\frac{v_{{uut}_{0}}}{v_{ref}}\frac{r_{uut} + {{\eta\delta}\; r}}{r_{ref} + {\left( {\eta - 1} \right)\delta\; r}}{\mathbb{e}}^{j\;{k{({r_{uut} - r_{ref} - {\delta\; r}})}}}}$where M_(uut) ₀ is the complex sensitivity of the acoustic sensor,M_(ref) is the complex sensitivity of the reference hydrophone, v_(uut)₀ is the complex voltage measured on the acoustic sensor, v_(ref) is thecomplex voltage measured on the reference hydrophone, k is the wavenumber, r_(uut) is the source-to-sensor distance, r_(ref) is thesource-to-reference distance, and δr is the range difference error. 3.The method in accordance with claim 1 wherein phases of complexsensitivities are computed using a nominal distance from the acousticsource to the reference hydrophone r_(ref), a nominal distance from theacoustic source to the vector sensor r_(uut) a range difference errorδr, and a acoustic wave number k=2πf/C where sound speed C is providedby an independent measurement to arbitrary precision.